LMFDB - Embedded newform 29.12.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,12,Mod(1,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	29.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$22.2819522362$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 23517 x^{12} - 42196 x^{11} + 214206700 x^{10} + 532863376 x^{9} - 951901011680 x^{8} + \cdots + 30\!\cdots\!04 $ x^14 - 23517x^12 - 42196x^11 + 214206700x^10 + 532863376x^9 - 951901011680x^8 - 1439668569088x^7 + 2125122050961664x^6 - 3617975849298944x^5 - 2179155305696991232x^4 + 15507015861824716800x^3 + 709645914927917694976x^2 - 9478460460037847384064x + 30797548279705794248704
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-26.9644$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-26.9644 q^{2} +724.855 q^{3} -1320.92 q^{4} -9762.32 q^{5} -19545.3 q^{6} -73001.2 q^{7} +90841.0 q^{8} +348267. q^{9} +O(q^{10})$	\(q-26.9644 q^{2} +724.855 q^{3} -1320.92 q^{4} -9762.32 q^{5} -19545.3 q^{6} -73001.2 q^{7} +90841.0 q^{8} +348267. q^{9} +263235. q^{10} +527196. q^{11} -957474. q^{12} +961147. q^{13} +1.96844e6 q^{14} -7.07626e6 q^{15} +255766. q^{16} +1.07118e7 q^{17} -9.39083e6 q^{18} -7.28662e6 q^{19} +1.28952e7 q^{20} -5.29153e7 q^{21} -1.42156e7 q^{22} +3.19275e7 q^{23} +6.58465e7 q^{24} +4.64747e7 q^{25} -2.59168e7 q^{26} +1.24037e8 q^{27} +9.64287e7 q^{28} -2.05111e7 q^{29} +1.90807e8 q^{30} +1.82485e8 q^{31} -1.92939e8 q^{32} +3.82141e8 q^{33} -2.88838e8 q^{34} +7.12661e8 q^{35} -4.60033e8 q^{36} -7.13835e8 q^{37} +1.96480e8 q^{38} +6.96692e8 q^{39} -8.86819e8 q^{40} +1.96874e8 q^{41} +1.42683e9 q^{42} +5.26279e8 q^{43} -6.96384e8 q^{44} -3.39989e9 q^{45} -8.60906e8 q^{46} -9.33336e8 q^{47} +1.85393e8 q^{48} +3.35185e9 q^{49} -1.25316e9 q^{50} +7.76452e9 q^{51} -1.26960e9 q^{52} +5.28742e9 q^{53} -3.34459e9 q^{54} -5.14666e9 q^{55} -6.63151e9 q^{56} -5.28174e9 q^{57} +5.53072e8 q^{58} +2.52885e9 q^{59} +9.34717e9 q^{60} +1.85382e9 q^{61} -4.92061e9 q^{62} -2.54239e10 q^{63} +4.67868e9 q^{64} -9.38302e9 q^{65} -1.03042e10 q^{66} +1.28669e10 q^{67} -1.41495e10 q^{68} +2.31428e10 q^{69} -1.92165e10 q^{70} -1.02377e10 q^{71} +3.16369e10 q^{72} -5.32974e9 q^{73} +1.92482e10 q^{74} +3.36874e10 q^{75} +9.62503e9 q^{76} -3.84860e10 q^{77} -1.87859e10 q^{78} +3.32730e10 q^{79} -2.49687e9 q^{80} +2.82145e10 q^{81} -5.30860e9 q^{82} +9.76917e9 q^{83} +6.98968e10 q^{84} -1.04572e11 q^{85} -1.41908e10 q^{86} -1.48676e10 q^{87} +4.78910e10 q^{88} -8.30436e9 q^{89} +9.16762e10 q^{90} -7.01650e10 q^{91} -4.21736e10 q^{92} +1.32275e11 q^{93} +2.51669e10 q^{94} +7.11343e10 q^{95} -1.39853e11 q^{96} +7.76260e9 q^{97} -9.03809e10 q^{98} +1.83605e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) $ 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−26.9644	−0.595835	−0.297918	−	0.954592i	$-0.596292\pi$
$2$	−26.9644	−0.595835	−0.297918	+	0.954592i	$0.596292\pi$
$3$	724.855	1.72220	0.861101	−	0.508434i	$-0.169776\pi$
$3$	724.855	1.72220	0.861101	+	0.508434i	$0.169776\pi$
$4$	−1320.92	−0.644980
$5$	−9762.32	−1.39707	−0.698534	−	0.715576i	$-0.746164\pi$
$5$	−9762.32	−1.39707	−0.698534	+	0.715576i	$0.746164\pi$
$6$	−19545.3	−1.02615
$7$	−73001.2	−1.64169	−0.820845	−	0.571151i	$-0.806497\pi$
$7$	−73001.2	−1.64169	−0.820845	+	0.571151i	$0.806497\pi$
$8$	90841.0	0.980137
$9$	348267.	1.96598
$10$	263235.	0.832423
$11$	527196.	0.986990	0.493495	−	0.869749i	$-0.335719\pi$
$11$	527196.	0.986990	0.493495	+	0.869749i	$0.335719\pi$
$12$	−957474.	−1.11079
$13$	961147.	0.717962	0.358981	−	0.933345i	$-0.383124\pi$
$13$	961147.	0.717962	0.358981	+	0.933345i	$0.383124\pi$
$14$	1.96844e6	0.978177
$15$	−7.07626e6	−2.40603
$16$	255766.	0.0609794
$17$	1.07118e7	1.82976	0.914881	−	0.403724i	$-0.132284\pi$
$17$	1.07118e7	1.82976	0.914881	+	0.403724i	$0.132284\pi$
$18$	−9.39083e6	−1.17140
$19$	−7.28662e6	−0.675120	−0.337560	−	0.941304i	$-0.609602\pi$
$19$	−7.28662e6	−0.675120	−0.337560	+	0.941304i	$0.609602\pi$
$20$	1.28952e7	0.901082
$21$	−5.29153e7	−2.82732
$22$	−1.42156e7	−0.588084
$23$	3.19275e7	1.03433	0.517167	−	0.855884i	$-0.326986\pi$
$23$	3.19275e7	1.03433	0.517167	+	0.855884i	$0.326986\pi$
$24$	6.58465e7	1.68799
$25$	4.64747e7	0.951802
$26$	−2.59168e7	−0.427787
$27$	1.24037e8	1.66361
$28$	9.64287e7	1.05886
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	1.90807e8	1.43360
$31$	1.82485e8	1.14482	0.572412	−	0.819966i	$-0.306008\pi$
$31$	1.82485e8	1.14482	0.572412	+	0.819966i	$0.306008\pi$
$32$	−1.92939e8	−1.01647
$33$	3.82141e8	1.69980
$34$	−2.88838e8	−1.09024
$35$	7.12661e8	2.29355
$36$	−4.60033e8	−1.26802
$37$	−7.13835e8	−1.69234	−0.846172	−	0.532911i	$-0.821098\pi$
$37$	−7.13835e8	−1.69234	−0.846172	+	0.532911i	$0.821098\pi$
$38$	1.96480e8	0.402261
$39$	6.96692e8	1.23648
$40$	−8.86819e8	−1.36932
$41$	1.96874e8	0.265386	0.132693	−	0.991157i	$-0.457638\pi$
$41$	1.96874e8	0.265386	0.132693	+	0.991157i	$0.457638\pi$
$42$	1.42683e9	1.68462
$43$	5.26279e8	0.545933	0.272967	−	0.962023i	$-0.411995\pi$
$43$	5.26279e8	0.545933	0.272967	+	0.962023i	$0.411995\pi$
$44$	−6.96384e8	−0.636589
$45$	−3.39989e9	−2.74661
$46$	−8.60906e8	−0.616293
$47$	−9.33336e8	−0.593608	−0.296804	−	0.954938i	$-0.595921\pi$
$47$	−9.33336e8	−0.593608	−0.296804	+	0.954938i	$0.595921\pi$
$48$	1.85393e8	0.105019
$49$	3.35185e9	1.69514
$50$	−1.25316e9	−0.567117
$51$	7.76452e9	3.15122
$52$	−1.26960e9	−0.463071
$53$	5.28742e9	1.73671	0.868353	−	0.495947i	$-0.165179\pi$
$53$	5.28742e9	1.73671	0.868353	+	0.495947i	$0.165179\pi$
$54$	−3.34459e9	−0.991237
$55$	−5.14666e9	−1.37889
$56$	−6.63151e9	−1.60908
$57$	−5.28174e9	−1.16269
$58$	5.53072e8	0.110644
$59$	2.52885e9	0.460507	0.230254	−	0.973131i	$-0.426044\pi$
$59$	2.52885e9	0.460507	0.230254	+	0.973131i	$0.426044\pi$
$60$	9.34717e9	1.55184
$61$	1.85382e9	0.281031	0.140515	−	0.990078i	$-0.455124\pi$
$61$	1.85382e9	0.281031	0.140515	+	0.990078i	$0.455124\pi$
$62$	−4.92061e9	−0.682127
$63$	−2.54239e10	−3.22753
$64$	4.67868e9	0.544670
$65$	−9.38302e9	−1.00304
$66$	−1.03042e10	−1.01280
$67$	1.28669e10	1.16429	0.582145	−	0.813085i	$-0.302214\pi$
$67$	1.28669e10	1.16429	0.582145	+	0.813085i	$0.302214\pi$
$68$	−1.41495e10	−1.18016
$69$	2.31428e10	1.78133
$70$	−1.92165e10	−1.36658
$71$	−1.02377e10	−0.673414	−0.336707	−	0.941609i	$-0.609313\pi$
$71$	−1.02377e10	−0.673414	−0.336707	+	0.941609i	$0.609313\pi$
$72$	3.16369e10	1.92693
$73$	−5.32974e9	−0.300906	−0.150453	−	0.988617i	$-0.548073\pi$
$73$	−5.32974e9	−0.300906	−0.150453	+	0.988617i	$0.548073\pi$
$74$	1.92482e10	1.00836
$75$	3.36874e10	1.63919
$76$	9.62503e9	0.435439
$77$	−3.84860e10	−1.62033
$78$	−1.87859e10	−0.736736
$79$	3.32730e10	1.21659	0.608294	−	0.793712i	$-0.291854\pi$
$79$	3.32730e10	1.21659	0.608294	+	0.793712i	$0.291854\pi$
$80$	−2.49687e9	−0.0851924
$81$	2.82145e10	0.899092
$82$	−5.30860e9	−0.158126
$83$	9.76917e9	0.272225	0.136113	−	0.990693i	$-0.456539\pi$
$83$	9.76917e9	0.272225	0.136113	+	0.990693i	$0.456539\pi$
$84$	6.98968e10	1.82357
$85$	−1.04572e11	−2.55630
$86$	−1.41908e10	−0.325286
$87$	−1.48676e10	−0.319805
$88$	4.78910e10	0.967386
$89$	−8.30436e9	−0.157638	−0.0788190	−	0.996889i	$-0.525115\pi$
$89$	−8.30436e9	−0.157638	−0.0788190	+	0.996889i	$0.525115\pi$
$90$	9.16762e10	1.63653
$91$	−7.01650e10	−1.17867
$92$	−4.21736e10	−0.667125
$93$	1.32275e11	1.97162
$94$	2.51669e10	0.353693
$95$	7.11343e10	0.943190
$96$	−1.39853e11	−1.75057
$97$	7.76260e9	0.0917830	0.0458915	−	0.998946i	$-0.485387\pi$
$97$	7.76260e9	0.0917830	0.0458915	+	0.998946i	$0.485387\pi$
$98$	−9.03809e10	−1.01003
$99$	1.83605e11	1.94040
$100$	−6.13893e10	−0.613893
$101$	3.59578e10	0.340428	0.170214	−	0.985407i	$-0.445554\pi$
$101$	3.59578e10	0.340428	0.170214	+	0.985407i	$0.445554\pi$
$102$	−2.09366e11	−1.87761
$103$	−3.18556e10	−0.270758	−0.135379	−	0.990794i	$-0.543225\pi$
$103$	−3.18556e10	−0.270758	−0.135379	+	0.990794i	$0.543225\pi$
$104$	8.73116e10	0.703702
$105$	5.16576e11	3.94996
$106$	−1.42572e11	−1.03479
$107$	4.08468e10	0.281544	0.140772	−	0.990042i	$-0.455041\pi$
$107$	4.08468e10	0.281544	0.140772	+	0.990042i	$0.455041\pi$
$108$	−1.63843e11	−1.07299
$109$	6.15012e10	0.382858	0.191429	−	0.981506i	$-0.438688\pi$
$109$	6.15012e10	0.382858	0.191429	+	0.981506i	$0.438688\pi$
$110$	1.38777e11	0.821593
$111$	−5.17427e11	−2.91456
$112$	−1.86713e10	−0.100109
$113$	3.22442e10	0.164634	0.0823172	−	0.996606i	$-0.473768\pi$
$113$	3.22442e10	0.164634	0.0823172	+	0.996606i	$0.473768\pi$
$114$	1.42419e11	0.692774
$115$	−3.11686e11	−1.44504
$116$	2.70936e10	0.119770
$117$	3.34736e11	1.41150
$118$	−6.81889e10	−0.274386
$119$	−7.81977e11	−3.00390
$120$	−6.42814e11	−2.35824
$121$	−7.37565e9	−0.0258512
$122$	−4.99873e10	−0.167448
$123$	1.42705e11	0.457048
$124$	−2.41048e11	−0.738389
$125$	2.29750e10	0.0673366
$126$	6.85542e11	1.92307
$127$	−2.36938e10	−0.0636376	−0.0318188	−	0.999494i	$-0.510130\pi$
$127$	−2.36938e10	−0.0636376	−0.0318188	+	0.999494i	$0.510130\pi$
$128$	2.68981e11	0.691937
$129$	3.81476e11	0.940207
$130$	2.53008e11	0.597648
$131$	−3.46312e11	−0.784288	−0.392144	−	0.919904i	$-0.628266\pi$
$131$	−3.46312e11	−0.784288	−0.392144	+	0.919904i	$0.628266\pi$
$132$	−5.04777e11	−1.09633
$133$	5.31932e11	1.10834
$134$	−3.46947e11	−0.693725
$135$	−1.21089e12	−2.32418
$136$	9.73073e11	1.79342
$137$	8.72226e11	1.54407	0.772033	−	0.635583i	$-0.219240\pi$
$137$	8.72226e11	1.54407	0.772033	+	0.635583i	$0.219240\pi$
$138$	−6.24032e11	−1.06138
$139$	4.41116e11	0.721060	0.360530	−	0.932748i	$-0.382596\pi$
$139$	4.41116e11	0.721060	0.360530	+	0.932748i	$0.382596\pi$
$140$	−9.41368e11	−1.47930
$141$	−6.76533e11	−1.02231
$142$	2.76054e11	0.401244
$143$	5.06713e11	0.708621
$144$	8.90750e10	0.119884
$145$	2.00236e11	0.259429
$146$	1.43713e11	0.179290
$147$	2.42961e12	2.91938
$148$	9.42918e11	1.09153
$149$	−5.19974e11	−0.580039	−0.290020	−	0.957021i	$-0.593662\pi$
$149$	−5.19974e11	−0.580039	−0.290020	+	0.957021i	$0.593662\pi$
$150$	−9.08361e11	−0.976690
$151$	4.38965e11	0.455048	0.227524	−	0.973773i	$-0.426937\pi$
$151$	4.38965e11	0.455048	0.227524	+	0.973773i	$0.426937\pi$
$152$	−6.61924e11	−0.661711
$153$	3.73058e12	3.59727
$154$	1.03775e12	0.965451
$155$	−1.78148e12	−1.59940
$156$	−9.20274e11	−0.797502
$157$	7.38035e11	0.617489	0.308744	−	0.951145i	$-0.400091\pi$
$157$	7.38035e11	0.617489	0.308744	+	0.951145i	$0.400091\pi$
$158$	−8.97189e11	−0.724886
$159$	3.83261e12	2.99096
$160$	1.88353e12	1.42008
$161$	−2.33074e12	−1.69806
$162$	−7.60787e11	−0.535711
$163$	−1.40563e12	−0.956837	−0.478418	−	0.878132i	$-0.658790\pi$
$163$	−1.40563e12	−0.956837	−0.478418	+	0.878132i	$0.658790\pi$
$164$	−2.60055e11	−0.171169
$165$	−3.73058e12	−2.37473
$166$	−2.63420e11	−0.162201
$167$	2.66616e11	0.158835	0.0794175	−	0.996841i	$-0.474694\pi$
$167$	2.66616e11	0.158835	0.0794175	+	0.996841i	$0.474694\pi$
$168$	−4.80688e12	−2.77116
$169$	−8.68356e11	−0.484530
$170$	2.81973e12	1.52314
$171$	−2.53769e12	−1.32727
$172$	−6.95172e11	−0.352116
$173$	−3.97214e11	−0.194882	−0.0974408	−	0.995241i	$-0.531066\pi$
$173$	−3.97214e11	−0.194882	−0.0974408	+	0.995241i	$0.531066\pi$
$174$	4.00896e11	0.190551
$175$	−3.39271e12	−1.56256
$176$	1.34839e11	0.0601861
$177$	1.83305e12	0.793086
$178$	2.23922e11	0.0939263
$179$	5.69325e11	0.231563	0.115781	−	0.993275i	$-0.463063\pi$
$179$	5.69325e11	0.231563	0.115781	+	0.993275i	$0.463063\pi$
$180$	4.49099e12	1.77151
$181$	2.58773e12	0.990116	0.495058	−	0.868860i	$-0.335147\pi$
$181$	2.58773e12	0.990116	0.495058	+	0.868860i	$0.335147\pi$
$182$	1.89196e12	0.702294
$183$	1.34375e12	0.483992
$184$	2.90032e12	1.01379
$185$	6.96868e12	2.36432
$186$	−3.56673e12	−1.17476
$187$	5.64724e12	1.80596
$188$	1.23286e12	0.382865
$189$	−9.05487e12	−2.73113
$190$	−1.91810e12	−0.561986
$191$	−6.37068e12	−1.81344	−0.906718	−	0.421736i	$-0.861421\pi$
$191$	−6.37068e12	−1.81344	−0.906718	+	0.421736i	$0.861421\pi$
$192$	3.39136e12	0.938032
$193$	6.33363e11	0.170250	0.0851250	−	0.996370i	$-0.472871\pi$
$193$	6.33363e11	0.170250	0.0851250	+	0.996370i	$0.472871\pi$
$194$	−2.09314e11	−0.0546876
$195$	−6.80133e12	−1.72744
$196$	−4.42753e12	−1.09333
$197$	−2.73278e11	−0.0656206	−0.0328103	−	0.999462i	$-0.510446\pi$
$197$	−2.73278e11	−0.0656206	−0.0328103	+	0.999462i	$0.510446\pi$
$198$	−4.95081e12	−1.15616
$199$	−3.22687e12	−0.732975	−0.366487	−	0.930423i	$-0.619440\pi$
$199$	−3.22687e12	−0.732975	−0.366487	+	0.930423i	$0.619440\pi$
$200$	4.22181e12	0.932896
$201$	9.32660e12	2.00514
$202$	−9.69581e11	−0.202839
$203$	1.49734e12	0.304854
$204$	−1.02563e13	−2.03247
$205$	−1.92195e12	−0.370762
$206$	8.58970e11	0.161327
$207$	1.11193e13	2.03348
$208$	2.45829e11	0.0437809
$209$	−3.84148e12	−0.666337
$210$	−1.39292e13	−2.35353
$211$	7.26519e12	1.19590	0.597948	−	0.801535i	$-0.295983\pi$
$211$	7.26519e12	1.19590	0.597948	+	0.801535i	$0.295983\pi$
$212$	−6.98425e12	−1.12014
$213$	−7.42086e12	−1.15975
$214$	−1.10141e12	−0.167754
$215$	−5.13770e12	−0.762706
$216$	1.12677e13	1.63057
$217$	−1.33217e13	−1.87945
$218$	−1.65834e12	−0.228120
$219$	−3.86329e12	−0.518220
$220$	6.79832e12	0.889358
$221$	1.02956e13	1.31370
$222$	1.39521e13	1.73660
$223$	1.09328e13	1.32756	0.663779	−	0.747929i	$-0.268952\pi$
$223$	1.09328e13	1.32756	0.663779	+	0.747929i	$0.268952\pi$
$224$	1.40848e13	1.66873
$225$	1.61856e13	1.87122
$226$	−8.69448e11	−0.0980950
$227$	−4.04906e12	−0.445874	−0.222937	−	0.974833i	$-0.571564\pi$
$227$	−4.04906e12	−0.445874	−0.222937	+	0.974833i	$0.571564\pi$
$228$	6.97675e12	0.749914
$229$	2.14875e12	0.225471	0.112736	−	0.993625i	$-0.464039\pi$
$229$	2.14875e12	0.225471	0.112736	+	0.993625i	$0.464039\pi$
$230$	8.40443e12	0.861004
$231$	−2.78967e13	−2.79054
$232$	−1.86325e12	−0.182007
$233$	−1.64319e13	−1.56758	−0.783791	−	0.621025i	$-0.786716\pi$
$233$	−1.64319e13	−1.56758	−0.783791	+	0.621025i	$0.786716\pi$
$234$	−9.02597e12	−0.841021
$235$	9.11152e12	0.829311
$236$	−3.34040e12	−0.297018
$237$	2.41181e13	2.09521
$238$	2.10856e13	1.78983
$239$	8.61687e12	0.714762	0.357381	−	0.933959i	$-0.383670\pi$
$239$	8.61687e12	0.714762	0.357381	+	0.933959i	$0.383670\pi$
$240$	−1.80987e12	−0.146719
$241$	1.64304e13	1.30183	0.650917	−	0.759149i	$-0.274385\pi$
$241$	1.64304e13	1.30183	0.650917	+	0.759149i	$0.274385\pi$
$242$	1.98880e11	0.0154031
$243$	−1.52143e12	−0.115191
$244$	−2.44875e12	−0.181259
$245$	−3.27219e13	−2.36823
$246$	−3.84796e12	−0.272325
$247$	−7.00351e12	−0.484711
$248$	1.65772e13	1.12208
$249$	7.08123e12	0.468827
$250$	−6.19509e11	−0.0401215
$251$	−1.74008e13	−1.10246	−0.551231	−	0.834353i	$-0.685842\pi$
$251$	−1.74008e13	−1.10246	−0.551231	+	0.834353i	$0.685842\pi$
$252$	3.35830e13	2.08169
$253$	1.68320e13	1.02088
$254$	6.38889e11	0.0379175
$255$	−7.57997e13	−4.40247
$256$	−1.68349e13	−0.956951
$257$	4.12206e12	0.229341	0.114671	−	0.993404i	$-0.463419\pi$
$257$	4.12206e12	0.229341	0.114671	+	0.993404i	$0.463419\pi$
$258$	−1.02863e13	−0.560209
$259$	5.21108e13	2.77830
$260$	1.23942e13	0.646943
$261$	−7.14336e12	−0.365073
$262$	9.33811e12	0.467306
$263$	−5.28636e12	−0.259060	−0.129530	−	0.991576i	$-0.541347\pi$
$263$	−5.28636e12	−0.259060	−0.129530	+	0.991576i	$0.541347\pi$
$264$	3.47140e13	1.66603
$265$	−5.16174e13	−2.42630
$266$	−1.43432e13	−0.660387
$267$	−6.01945e12	−0.271484
$268$	−1.69961e13	−0.750943
$269$	−3.09159e13	−1.33827	−0.669135	−	0.743141i	$-0.733335\pi$
$269$	−3.09159e13	−1.33827	−0.669135	+	0.743141i	$0.733335\pi$
$270$	3.26510e13	1.38483
$271$	−3.26332e13	−1.35622	−0.678108	−	0.734962i	$-0.737200\pi$
$271$	−3.26332e13	−1.35622	−0.678108	+	0.734962i	$0.737200\pi$
$272$	2.73972e12	0.111578
$273$	−5.08594e13	−2.02991
$274$	−2.35191e13	−0.920009
$275$	2.45013e13	0.939418
$276$	−3.05697e13	−1.14892
$277$	−3.44295e13	−1.26850	−0.634252	−	0.773126i	$-0.718692\pi$
$277$	−3.44295e13	−1.26850	−0.634252	+	0.773126i	$0.718692\pi$
$278$	−1.18944e13	−0.429633
$279$	6.35537e13	2.25070
$280$	6.47389e13	2.24800
$281$	−2.90133e13	−0.987900	−0.493950	−	0.869490i	$-0.664447\pi$
$281$	−2.90133e13	−0.987900	−0.493950	+	0.869490i	$0.664447\pi$
$282$	1.82423e13	0.609130
$283$	5.24778e13	1.71850	0.859252	−	0.511553i	$-0.170930\pi$
$283$	5.24778e13	1.71850	0.859252	+	0.511553i	$0.170930\pi$
$284$	1.35232e13	0.434339
$285$	5.15620e13	1.62436
$286$	−1.36632e13	−0.422222
$287$	−1.43721e13	−0.435681
$288$	−6.71943e13	−1.99836
$289$	8.04714e13	2.34803
$290$	−5.39926e12	−0.154577
$291$	5.62675e12	0.158069
$292$	7.04016e12	0.194078
$293$	−3.27363e13	−0.885640	−0.442820	−	0.896610i	$-0.646022\pi$
$293$	−3.27363e13	−0.885640	−0.442820	+	0.896610i	$0.646022\pi$
$294$	−6.55130e13	−1.73947
$295$	−2.46874e13	−0.643360
$296$	−6.48455e13	−1.65873
$297$	6.53920e13	1.64197
$298$	1.40208e13	0.345608
$299$	3.06870e13	0.742613
$300$	−4.44983e13	−1.05725
$301$	−3.84190e13	−0.896253
$302$	−1.18365e13	−0.271134
$303$	2.60642e13	0.586286
$304$	−1.86367e12	−0.0411684
$305$	−1.80976e13	−0.392619
$306$	−1.00593e14	−2.14338
$307$	−5.53299e13	−1.15797	−0.578987	−	0.815336i	$-0.696552\pi$
$307$	−5.53299e13	−1.15797	−0.578987	+	0.815336i	$0.696552\pi$
$308$	5.08369e13	1.04508
$309$	−2.30907e13	−0.466300
$310$	4.80366e13	0.952978
$311$	−5.73924e12	−0.111859	−0.0559297	−	0.998435i	$-0.517812\pi$
$311$	−5.73924e12	−0.111859	−0.0559297	+	0.998435i	$0.517812\pi$
$312$	6.32882e13	1.21192
$313$	5.35664e13	1.00786	0.503928	−	0.863746i	$-0.331888\pi$
$313$	5.35664e13	1.00786	0.503928	+	0.863746i	$0.331888\pi$
$314$	−1.99007e13	−0.367922
$315$	2.48196e14	4.50908
$316$	−4.39510e13	−0.784675
$317$	9.21660e13	1.61713	0.808564	−	0.588408i	$-0.200245\pi$
$317$	9.21660e13	1.61713	0.808564	+	0.588408i	$0.200245\pi$
$318$	−1.03344e14	−1.78212
$319$	−1.08134e13	−0.183279
$320$	−4.56748e13	−0.760942
$321$	2.96080e13	0.484876
$322$	6.28472e13	1.01176
$323$	−7.80530e13	−1.23531
$324$	−3.72690e13	−0.579897
$325$	4.46690e13	0.683358
$326$	3.79019e13	0.570117
$327$	4.45794e13	0.659359
$328$	1.78843e13	0.260115
$329$	6.81347e13	0.974520
$330$	1.00593e14	1.41495
$331$	8.06249e13	1.11536	0.557680	−	0.830056i	$-0.311692\pi$
$331$	8.06249e13	1.11536	0.557680	+	0.830056i	$0.311692\pi$
$332$	−1.29043e13	−0.175580
$333$	−2.48605e14	−3.32711
$334$	−7.18916e12	−0.0946395
$335$	−1.25610e14	−1.62659
$336$	−1.35339e13	−0.172408
$337$	2.30056e13	0.288317	0.144158	−	0.989555i	$-0.453953\pi$
$337$	2.30056e13	0.288317	0.144158	+	0.989555i	$0.453953\pi$
$338$	2.34147e13	0.288700
$339$	2.33724e13	0.283534
$340$	1.38132e14	1.64876
$341$	9.62056e13	1.12993
$342$	6.84274e13	0.790836
$343$	−1.00342e14	−1.14121
$344$	4.78077e13	0.535090
$345$	−2.25927e14	−2.48865
$346$	1.07107e13	0.116117
$347$	1.83229e14	1.95516	0.977582	−	0.210556i	$-0.0675276\pi$
$347$	1.83229e14	1.95516	0.977582	+	0.210556i	$0.0675276\pi$
$348$	1.96389e13	0.206268
$349$	7.48267e13	0.773601	0.386800	−	0.922163i	$-0.373580\pi$
$349$	7.48267e13	0.773601	0.386800	+	0.922163i	$0.373580\pi$
$350$	9.14825e13	0.931030
$351$	1.19218e14	1.19441
$352$	−1.01717e14	−1.00325
$353$	2.36693e13	0.229839	0.114919	−	0.993375i	$-0.463339\pi$
$353$	2.36693e13	0.229839	0.114919	+	0.993375i	$0.463339\pi$
$354$	−4.94270e13	−0.472549
$355$	9.99438e13	0.940806
$356$	1.09694e13	0.101673
$357$	−5.66820e14	−5.17332
$358$	−1.53515e13	−0.137973
$359$	1.86929e14	1.65447	0.827233	−	0.561860i	$-0.189914\pi$
$359$	1.86929e14	1.65447	0.827233	+	0.561860i	$0.189914\pi$
$360$	−3.08850e14	−2.69205
$361$	−6.33955e13	−0.544213
$362$	−6.97765e13	−0.589946
$363$	−5.34628e12	−0.0445210
$364$	9.26822e13	0.760219
$365$	5.20306e13	0.420386
$366$	−3.62335e13	−0.288379
$367$	1.20171e14	0.942187	0.471094	−	0.882083i	$-0.343859\pi$
$367$	1.20171e14	0.942187	0.471094	+	0.882083i	$0.343859\pi$
$368$	8.16596e12	0.0630731
$369$	6.85648e13	0.521743
$370$	−1.87907e14	−1.40875
$371$	−3.85988e14	−2.85113
$372$	−1.74725e14	−1.27165
$373$	4.94917e13	0.354922	0.177461	−	0.984128i	$-0.443212\pi$
$373$	4.94917e13	0.354922	0.177461	+	0.984128i	$0.443212\pi$
$374$	−1.52275e14	−1.07605
$375$	1.66536e13	0.115967
$376$	−8.47852e13	−0.581818
$377$	−1.97142e13	−0.133322
$378$	2.44160e14	1.62730
$379$	−1.66037e14	−1.09066	−0.545328	−	0.838223i	$-0.683595\pi$
$379$	−1.66037e14	−1.09066	−0.545328	+	0.838223i	$0.683595\pi$
$380$	−9.39626e13	−0.608338
$381$	−1.71745e13	−0.109597
$382$	1.71782e14	1.08051
$383$	2.31278e14	1.43397	0.716986	−	0.697088i	$-0.245521\pi$
$383$	2.31278e14	1.43397	0.716986	+	0.697088i	$0.245521\pi$
$384$	1.94972e14	1.19166
$385$	3.75712e14	2.26371
$386$	−1.70783e13	−0.101441
$387$	1.83286e14	1.07329
$388$	−1.02538e13	−0.0591982
$389$	−2.89490e14	−1.64782	−0.823912	−	0.566717i	$-0.808213\pi$
$389$	−2.89490e14	−1.64782	−0.823912	+	0.566717i	$0.808213\pi$
$390$	1.83394e14	1.02927
$391$	3.42001e14	1.89259
$392$	3.04486e14	1.66147
$393$	−2.51026e14	−1.35070
$394$	7.36878e12	0.0390991
$395$	−3.24822e14	−1.69966
$396$	−2.42528e14	−1.25152
$397$	−3.23449e14	−1.64611	−0.823054	−	0.567963i	$-0.807732\pi$
$397$	−3.23449e14	−1.64611	−0.823054	+	0.567963i	$0.807732\pi$
$398$	8.70106e13	0.436732
$399$	3.85573e14	1.90878
$400$	1.18867e13	0.0580403
$401$	−4.43993e12	−0.0213837	−0.0106918	−	0.999943i	$-0.503403\pi$
$401$	−4.43993e12	−0.0213837	−0.0106918	+	0.999943i	$0.503403\pi$
$402$	−2.51486e14	−1.19473
$403$	1.75395e14	0.821940
$404$	−4.74973e13	−0.219569
$405$	−2.75439e14	−1.25609
$406$	−4.03749e13	−0.181643
$407$	−3.76331e14	−1.67033
$408$	7.05337e14	3.08863
$409$	−3.23716e14	−1.39858	−0.699288	−	0.714840i	$-0.746500\pi$
$409$	−3.23716e14	−1.39858	−0.699288	+	0.714840i	$0.746500\pi$
$410$	5.18243e13	0.220913
$411$	6.32237e14	2.65919
$412$	4.20787e13	0.174634
$413$	−1.84609e14	−0.756010
$414$	−2.99825e14	−1.21162
$415$	−9.53697e13	−0.380317
$416$	−1.85443e14	−0.729788
$417$	3.19745e14	1.24181
$418$	1.03583e14	0.397027
$419$	−2.53233e14	−0.957949	−0.478975	−	0.877829i	$-0.658991\pi$
$419$	−2.53233e14	−0.957949	−0.478975	+	0.877829i	$0.658991\pi$
$420$	−6.82355e14	−2.54765
$421$	2.53115e14	0.932752	0.466376	−	0.884587i	$-0.345559\pi$
$421$	2.53115e14	0.932752	0.466376	+	0.884587i	$0.345559\pi$
$422$	−1.95902e14	−0.712558
$423$	−3.25050e14	−1.16702
$424$	4.80314e14	1.70221
$425$	4.97829e14	1.74157
$426$	2.00099e14	0.691023
$427$	−1.35331e14	−0.461365
$428$	−5.39553e13	−0.181591
$429$	3.67294e14	1.22039
$430$	1.38535e14	0.454448
$431$	−2.18661e13	−0.0708186	−0.0354093	−	0.999373i	$-0.511273\pi$
$431$	−2.18661e13	−0.0708186	−0.0354093	+	0.999373i	$0.511273\pi$
$432$	3.17245e13	0.101446
$433$	−3.03868e14	−0.959405	−0.479703	−	0.877431i	$-0.659255\pi$
$433$	−3.03868e14	−0.959405	−0.479703	+	0.877431i	$0.659255\pi$
$434$	3.59211e14	1.11984
$435$	1.45142e14	0.446789
$436$	−8.12381e13	−0.246936
$437$	−2.32643e14	−0.698300
$438$	1.04171e14	0.308774
$439$	−6.01002e14	−1.75923	−0.879613	−	0.475691i	$-0.842198\pi$
$439$	−6.01002e14	−1.75923	−0.879613	+	0.475691i	$0.842198\pi$
$440$	−4.67528e14	−1.35150
$441$	1.16734e15	3.33262
$442$	−2.77616e14	−0.782749
$443$	5.86968e13	0.163453	0.0817267	−	0.996655i	$-0.473957\pi$
$443$	5.86968e13	0.163453	0.0817267	+	0.996655i	$0.473957\pi$
$444$	6.83479e14	1.87983
$445$	8.10698e13	0.220231
$446$	−2.94796e14	−0.791006
$447$	−3.76906e14	−0.998944
$448$	−3.41550e14	−0.894179
$449$	5.21407e14	1.34841	0.674205	−	0.738544i	$-0.264486\pi$
$449$	5.21407e14	1.34841	0.674205	+	0.738544i	$0.264486\pi$
$450$	−4.36436e14	−1.11494
$451$	1.03791e14	0.261933
$452$	−4.25920e13	−0.106186
$453$	3.18186e14	0.783684
$454$	1.09181e14	0.265668
$455$	6.84972e14	1.64668
$456$	−4.79798e14	−1.13960
$457$	−6.42763e14	−1.50838	−0.754192	−	0.656654i	$-0.771971\pi$
$457$	−6.42763e14	−1.50838	−0.754192	+	0.656654i	$0.771971\pi$
$458$	−5.79399e13	−0.134344
$459$	1.32867e15	3.04401
$460$	4.11712e14	0.932020
$461$	3.23532e14	0.723706	0.361853	−	0.932235i	$-0.382144\pi$
$461$	3.23532e14	0.723706	0.361853	+	0.932235i	$0.382144\pi$
$462$	7.52220e14	1.66270
$463$	−1.24719e14	−0.272418	−0.136209	−	0.990680i	$-0.543492\pi$
$463$	−1.24719e14	−0.272418	−0.136209	+	0.990680i	$0.543492\pi$
$464$	−5.24606e12	−0.0113236
$465$	−1.29131e15	−2.75449
$466$	4.43077e14	0.934020
$467$	−5.09106e14	−1.06063	−0.530317	−	0.847800i	$-0.677927\pi$
$467$	−5.09106e14	−1.06063	−0.530317	+	0.847800i	$0.677927\pi$
$468$	−4.42159e14	−0.910388
$469$	−9.39296e14	−1.91140
$470$	−2.45687e14	−0.494133
$471$	5.34968e14	1.06344
$472$	2.29723e14	0.451360
$473$	2.77452e14	0.538831
$474$	−6.50331e14	−1.24840
$475$	−3.38643e14	−0.642580
$476$	1.03293e15	1.93746
$477$	1.84143e15	3.41433
$478$	−2.32349e14	−0.425880
$479$	−2.40774e14	−0.436279	−0.218140	−	0.975918i	$-0.569999\pi$
$479$	−2.40774e14	−0.436279	−0.218140	+	0.975918i	$0.569999\pi$
$480$	1.36529e15	2.44566
$481$	−6.86101e14	−1.21504
$482$	−4.43038e14	−0.775679
$483$	−1.68945e15	−2.92440
$484$	9.74264e12	0.0166735
$485$	−7.57809e13	−0.128227
$486$	4.10246e13	0.0686349
$487$	−1.79157e14	−0.296364	−0.148182	−	0.988960i	$-0.547342\pi$
$487$	−1.79157e14	−0.296364	−0.148182	+	0.988960i	$0.547342\pi$
$488$	1.68403e14	0.275449
$489$	−1.01887e15	−1.64787
$490$	8.82327e14	1.41108
$491$	−7.60805e14	−1.20316	−0.601582	−	0.798811i	$-0.705463\pi$
$491$	−7.60805e14	−1.20316	−0.601582	+	0.798811i	$0.705463\pi$
$492$	−1.88502e14	−0.294787
$493$	−2.19712e14	−0.339778
$494$	1.88846e14	0.288808
$495$	−1.79241e15	−2.71087
$496$	4.66736e13	0.0698107
$497$	7.47366e14	1.10554
$498$	−1.90941e14	−0.279343
$499$	−8.92013e13	−0.129068	−0.0645340	−	0.997916i	$-0.520556\pi$
$499$	−8.92013e13	−0.129068	−0.0645340	+	0.997916i	$0.520556\pi$
$500$	−3.03482e13	−0.0434308
$501$	1.93258e14	0.273546
$502$	4.69203e14	0.656886
$503$	−7.31710e14	−1.01325	−0.506623	−	0.862168i	$-0.669106\pi$
$503$	−7.31710e14	−1.01325	−0.506623	+	0.862168i	$0.669106\pi$
$504$	−2.30954e15	−3.16342
$505$	−3.51031e14	−0.475601
$506$	−4.53866e14	−0.608275
$507$	−6.29432e14	−0.834459
$508$	3.12975e13	0.0410450
$509$	1.47830e15	1.91786	0.958928	−	0.283648i	$-0.0915448\pi$
$509$	1.47830e15	1.91786	0.958928	+	0.283648i	$0.0915448\pi$
$510$	2.04390e15	2.62315
$511$	3.89078e14	0.493994
$512$	−9.69306e13	−0.121752
$513$	−9.03812e14	−1.12314
$514$	−1.11149e14	−0.136650
$515$	3.10985e14	0.378268
$516$	−5.03899e14	−0.606415
$517$	−4.92051e14	−0.585885
$518$	−1.40514e15	−1.65541
$519$	−2.87922e14	−0.335626
$520$	−8.52363e14	−0.983120
$521$	1.20839e15	1.37912	0.689559	−	0.724230i	$-0.257805\pi$
$521$	1.20839e15	1.37912	0.689559	+	0.724230i	$0.257805\pi$
$522$	1.92617e14	0.217523
$523$	7.65666e14	0.855618	0.427809	−	0.903869i	$-0.359286\pi$
$523$	7.65666e14	0.855618	0.427809	+	0.903869i	$0.359286\pi$
$524$	4.57450e14	0.505850
$525$	−2.45922e15	−2.69105
$526$	1.42544e14	0.154357
$527$	1.95475e15	2.09476
$528$	9.77387e13	0.103653
$529$	6.65527e13	0.0698489
$530$	1.39184e15	1.44567
$531$	8.80714e14	0.905347
$532$	−7.02639e14	−0.714856
$533$	1.89225e14	0.190537
$534$	1.62311e14	0.161760
$535$	−3.98759e14	−0.393337
$536$	1.16884e15	1.14116
$537$	4.12678e14	0.398798
$538$	8.33629e14	0.797389
$539$	1.76709e15	1.67309
$540$	1.59949e15	1.49905
$541$	−1.28775e15	−1.19466	−0.597331	−	0.801995i	$-0.703772\pi$
$541$	−1.28775e15	−1.19466	−0.597331	+	0.801995i	$0.703772\pi$
$542$	8.79937e14	0.808082
$543$	1.87572e15	1.70518
$544$	−2.06673e15	−1.85990
$545$	−6.00394e14	−0.534879
$546$	1.37139e15	1.20949
$547$	−1.35288e15	−1.18122	−0.590608	−	0.806959i	$-0.701112\pi$
$547$	−1.35288e15	−1.18122	−0.590608	+	0.806959i	$0.701112\pi$
$548$	−1.15214e15	−0.995891
$549$	6.45625e14	0.552500
$550$	−6.60663e14	−0.559739
$551$	1.49457e14	0.125367
$552$	2.10231e15	1.74595
$553$	−2.42897e15	−1.99726
$554$	9.28372e14	0.755820
$555$	5.05128e15	4.07184
$556$	−5.82678e14	−0.465069
$557$	−7.31800e14	−0.578347	−0.289174	−	0.957277i	$-0.593380\pi$
$557$	−7.31800e14	−0.578347	−0.289174	+	0.957277i	$0.593380\pi$
$558$	−1.71369e15	−1.34105
$559$	5.05832e14	0.391959
$560$	1.82275e14	0.139860
$561$	4.09343e15	3.11022
$562$	7.82328e14	0.588626
$563$	−1.05317e15	−0.784701	−0.392350	−	0.919816i	$-0.628338\pi$
$563$	−1.05317e15	−0.784701	−0.392350	+	0.919816i	$0.628338\pi$
$564$	8.93645e14	0.659371
$565$	−3.14778e14	−0.230006
$566$	−1.41503e15	−1.02395
$567$	−2.05969e15	−1.47603
$568$	−9.30005e14	−0.660038
$569$	3.00211e14	0.211013	0.105506	−	0.994419i	$-0.466354\pi$
$569$	3.00211e14	0.211013	0.105506	+	0.994419i	$0.466354\pi$
$570$	−1.39034e15	−0.967853
$571$	4.27085e14	0.294453	0.147226	−	0.989103i	$-0.452965\pi$
$571$	4.27085e14	0.294453	0.147226	+	0.989103i	$0.452965\pi$
$572$	−6.69328e14	−0.457047
$573$	−4.61782e15	−3.12310
$574$	3.87535e14	0.259594
$575$	1.48382e15	0.984482
$576$	1.62943e15	1.07081
$577$	−1.19904e15	−0.780491	−0.390246	−	0.920711i	$-0.627610\pi$
$577$	−1.19904e15	−0.780491	−0.390246	+	0.920711i	$0.627610\pi$
$578$	−2.16987e15	−1.39904
$579$	4.59096e14	0.293205
$580$	−2.64496e14	−0.167327
$581$	−7.13162e14	−0.446909
$582$	−1.51722e14	−0.0941831
$583$	2.78751e15	1.71411
$584$	−4.84159e14	−0.294929
$585$	−3.26780e15	−1.97196
$586$	8.82715e14	0.527696
$587$	2.27642e14	0.134816	0.0674081	−	0.997725i	$-0.478527\pi$
$587$	2.27642e14	0.134816	0.0674081	+	0.997725i	$0.478527\pi$
$588$	−3.20932e15	−1.88294
$589$	−1.32970e15	−0.772894
$590$	6.65682e14	0.383337
$591$	−1.98087e14	−0.113012
$592$	−1.82575e14	−0.103198
$593$	1.30877e15	0.732931	0.366465	−	0.930432i	$-0.380568\pi$
$593$	1.30877e15	0.732931	0.366465	+	0.930432i	$0.380568\pi$
$594$	−1.76326e15	−0.978341
$595$	7.63391e15	4.19666
$596$	6.86844e14	0.374114
$597$	−2.33901e15	−1.26233
$598$	−8.27457e14	−0.442475
$599$	−3.47000e15	−1.83858	−0.919289	−	0.393583i	$-0.871236\pi$
$599$	−3.47000e15	−1.83858	−0.919289	+	0.393583i	$0.871236\pi$
$600$	3.06020e15	1.60664
$601$	8.10553e14	0.421669	0.210835	−	0.977522i	$-0.432382\pi$
$601$	8.10553e14	0.421669	0.210835	+	0.977522i	$0.432382\pi$
$602$	1.03595e15	0.534019
$603$	4.48110e15	2.28897
$604$	−5.79838e14	−0.293497
$605$	7.20035e13	0.0361159
$606$	−7.02805e14	−0.349330
$607$	1.64596e15	0.810738	0.405369	−	0.914153i	$-0.367143\pi$
$607$	1.64596e15	0.810738	0.405369	+	0.914153i	$0.367143\pi$
$608$	1.40587e15	0.686240
$609$	1.08535e15	0.525020
$610$	4.87991e14	0.233937
$611$	−8.97074e14	−0.426188
$612$	−4.92779e15	−2.32017
$613$	3.36134e14	0.156848	0.0784241	−	0.996920i	$-0.475011\pi$
$613$	3.36134e14	0.156848	0.0784241	+	0.996920i	$0.475011\pi$
$614$	1.49194e15	0.689962
$615$	−1.39313e15	−0.638527
$616$	−3.49611e15	−1.58815
$617$	3.38253e14	0.152291	0.0761453	−	0.997097i	$-0.475739\pi$
$617$	3.38253e14	0.152291	0.0761453	+	0.997097i	$0.475739\pi$
$618$	6.22628e14	0.277838
$619$	2.95269e15	1.30593	0.652964	−	0.757389i	$-0.273525\pi$
$619$	2.95269e15	1.30593	0.652964	+	0.757389i	$0.273525\pi$
$620$	2.35319e15	1.03158
$621$	3.96019e15	1.72073
$622$	1.54755e14	0.0666498
$623$	6.06228e14	0.258793
$624$	1.78190e14	0.0753996
$625$	−2.49356e15	−1.04588
$626$	−1.44439e15	−0.600517
$627$	−2.78451e15	−1.14757
$628$	−9.74885e14	−0.398268
$629$	−7.64648e15	−3.09658
$630$	−6.69248e15	−2.68667
$631$	−1.12140e15	−0.446270	−0.223135	−	0.974788i	$-0.571629\pi$
$631$	−1.12140e15	−0.446270	−0.223135	+	0.974788i	$0.571629\pi$
$632$	3.02256e15	1.19242
$633$	5.26621e15	2.05958
$634$	−2.48520e15	−0.963543
$635$	2.31306e14	0.0889061
$636$	−5.06257e15	−1.92911
$637$	3.22163e15	1.21705
$638$	2.91577e14	0.109204
$639$	−3.56546e15	−1.32392
$640$	−2.62588e15	−0.966684
$641$	2.67869e15	0.977696	0.488848	−	0.872369i	$-0.337417\pi$
$641$	2.67869e15	0.977696	0.488848	+	0.872369i	$0.337417\pi$
$642$	−7.98362e14	−0.288906
$643$	−3.95841e14	−0.142023	−0.0710117	−	0.997475i	$-0.522623\pi$
$643$	−3.95841e14	−0.142023	−0.0710117	+	0.997475i	$0.522623\pi$
$644$	3.07872e15	1.09521
$645$	−3.72409e15	−1.31353
$646$	2.10465e15	0.736041
$647$	−1.33020e15	−0.461257	−0.230628	−	0.973042i	$-0.574078\pi$
$647$	−1.33020e15	−0.461257	−0.230628	+	0.973042i	$0.574078\pi$
$648$	2.56303e15	0.881234
$649$	1.33320e15	0.454516
$650$	−1.20447e15	−0.407169
$651$	−9.65626e15	−3.23678
$652$	1.85672e15	0.617141
$653$	−2.47371e15	−0.815316	−0.407658	−	0.913135i	$-0.633654\pi$
$653$	−2.47371e15	−0.815316	−0.407658	+	0.913135i	$0.633654\pi$
$654$	−1.20206e15	−0.392869
$655$	3.38081e15	1.09570
$656$	5.03538e13	0.0161831
$657$	−1.85617e15	−0.591574
$658$	−1.83721e15	−0.580654
$659$	1.68076e15	0.526788	0.263394	−	0.964688i	$-0.415158\pi$
$659$	1.68076e15	0.526788	0.263394	+	0.964688i	$0.415158\pi$
$660$	4.92779e15	1.53165
$661$	−4.24784e12	−0.00130936	−0.000654681	−	1.00000i	$-0.500208\pi$
$661$	−4.24784e12	−0.00130936	−0.000654681		1.00000i	$0.500208\pi$
$662$	−2.17400e15	−0.664571
$663$	7.46285e15	2.26246
$664$	8.87441e14	0.266818
$665$	−5.19289e15	−1.54842
$666$	6.70350e15	1.98241
$667$	−6.54869e14	−0.192071
$668$	−3.52179e14	−0.102445
$669$	7.92467e15	2.28632
$670$	3.38701e15	0.969181
$671$	9.77328e14	0.277374
$672$	1.02094e16	2.87389
$673$	−6.30522e14	−0.176042	−0.0880212	−	0.996119i	$-0.528054\pi$
$673$	−6.30522e14	−0.176042	−0.0880212	+	0.996119i	$0.528054\pi$
$674$	−6.20334e14	−0.171789
$675$	5.76459e15	1.58343
$676$	1.14703e15	0.312512
$677$	3.95433e15	1.06865	0.534325	−	0.845279i	$-0.320566\pi$
$677$	3.95433e15	1.06865	0.534325	+	0.845279i	$0.320566\pi$
$678$	−6.30223e14	−0.168939
$679$	−5.66679e14	−0.150679
$680$	−9.49945e15	−2.50553
$681$	−2.93498e15	−0.767885
$682$	−2.59413e15	−0.673252
$683$	5.20855e15	1.34092	0.670460	−	0.741946i	$-0.266097\pi$
$683$	5.20855e15	1.34092	0.670460	+	0.741946i	$0.266097\pi$
$684$	3.35208e15	0.856064
$685$	−8.51494e15	−2.15717
$686$	2.70567e15	0.679974
$687$	1.55753e15	0.388307
$688$	1.34604e14	0.0332907
$689$	5.08199e15	1.24689
$690$	6.09199e15	1.48282
$691$	−2.85739e15	−0.689987	−0.344994	−	0.938605i	$-0.612119\pi$
$691$	−2.85739e15	−0.689987	−0.344994	+	0.938605i	$0.612119\pi$
$692$	5.24688e14	0.125695
$693$	−1.34034e16	−3.18554
$694$	−4.94068e15	−1.16496
$695$	−4.30631e15	−1.00737
$696$	−1.35059e15	−0.313453
$697$	2.10888e15	0.485593
$698$	−2.01766e15	−0.460939
$699$	−1.19107e16	−2.69969
$700$	4.48150e15	1.00782
$701$	−2.20715e15	−0.492473	−0.246237	−	0.969210i	$-0.579194\pi$
$701$	−2.20715e15	−0.492473	−0.246237	+	0.969210i	$0.579194\pi$
$702$	−3.21465e15	−0.711671
$703$	5.20144e15	1.14254
$704$	2.46658e15	0.537584
$705$	6.60453e15	1.42824
$706$	−6.38228e14	−0.136946
$707$	−2.62496e15	−0.558877
$708$	−2.42131e15	−0.511525
$709$	6.44431e15	1.35090	0.675448	−	0.737408i	$-0.263950\pi$
$709$	6.44431e15	1.35090	0.675448	+	0.737408i	$0.263950\pi$
$710$	−2.69493e15	−0.560566
$711$	1.15879e16	2.39179
$712$	−7.54376e14	−0.154507
$713$	5.82629e15	1.18413
$714$	1.52840e16	3.08245
$715$	−4.94670e15	−0.989993
$716$	−7.52033e14	−0.149353
$717$	6.24598e15	1.23096
$718$	−5.04044e15	−0.985789
$719$	−4.58751e15	−0.890364	−0.445182	−	0.895440i	$-0.646861\pi$
$719$	−4.58751e15	−0.890364	−0.445182	+	0.895440i	$0.646861\pi$
$720$	−8.69578e14	−0.167487
$721$	2.32550e15	0.444501
$722$	1.70942e15	0.324261
$723$	1.19097e16	2.24202
$724$	−3.41818e15	−0.638605
$725$	−9.53249e14	−0.176745
$726$	1.44159e14	0.0265272
$727$	4.43822e15	0.810530	0.405265	−	0.914199i	$-0.367179\pi$
$727$	4.43822e15	0.810530	0.405265	+	0.914199i	$0.367179\pi$
$728$	−6.37386e15	−1.15526
$729$	−6.10093e15	−1.09747
$730$	−1.40298e15	−0.250481
$731$	5.63741e15	0.998928
$732$	−1.77499e15	−0.312165
$733$	−5.06352e15	−0.883854	−0.441927	−	0.897051i	$-0.645705\pi$
$733$	−5.06352e15	−0.883854	−0.441927	+	0.897051i	$0.645705\pi$
$734$	−3.24035e15	−0.561389
$735$	−2.37186e16	−4.07858
$736$	−6.16005e15	−1.05137
$737$	6.78336e15	1.14914
$738$	−1.84881e15	−0.310873
$739$	−9.41114e15	−1.57072	−0.785359	−	0.619041i	$-0.787521\pi$
$739$	−9.41114e15	−1.57072	−0.785359	+	0.619041i	$0.787521\pi$
$740$	−9.20507e15	−1.52494
$741$	−5.07653e15	−0.834770
$742$	1.04080e16	1.69881
$743$	−4.85818e14	−0.0787110	−0.0393555	−	0.999225i	$-0.512530\pi$
$743$	−4.85818e14	−0.0787110	−0.0393555	+	0.999225i	$0.512530\pi$
$744$	1.20160e16	1.93246
$745$	5.07615e15	0.810355
$746$	−1.33451e15	−0.211475
$747$	3.40228e15	0.535189
$748$	−7.45954e15	−1.16481
$749$	−2.98186e15	−0.462208
$750$	−4.49054e14	−0.0690974
$751$	1.05204e16	1.60699	0.803495	−	0.595311i	$-0.202971\pi$
$751$	1.05204e16	1.60699	0.803495	+	0.595311i	$0.202971\pi$
$752$	−2.38716e14	−0.0361979
$753$	−1.26130e16	−1.89866
$754$	5.31583e14	0.0794381
$755$	−4.28532e15	−0.635733
$756$	1.19608e16	1.76152
$757$	1.14757e16	1.67784	0.838921	−	0.544253i	$-0.183187\pi$
$757$	1.14757e16	1.67784	0.838921	+	0.544253i	$0.183187\pi$
$758$	4.47708e15	0.649852
$759$	1.22008e16	1.75816
$760$	6.46191e15	0.924455
$761$	−3.98160e15	−0.565512	−0.282756	−	0.959192i	$-0.591249\pi$
$761$	−3.98160e15	−0.565512	−0.282756	+	0.959192i	$0.591249\pi$
$762$	4.63102e14	0.0653016
$763$	−4.48966e15	−0.628534
$764$	8.41516e15	1.16963
$765$	−3.64191e16	−5.02564
$766$	−6.23627e15	−0.854411
$767$	2.43059e15	0.330627
$768$	−1.22028e16	−1.64806
$769$	4.23622e15	0.568047	0.284023	−	0.958817i	$-0.408331\pi$
$769$	4.23622e15	0.568047	0.284023	+	0.958817i	$0.408331\pi$
$770$	−1.01309e16	−1.34880
$771$	2.98790e15	0.394972
$772$	−8.36621e14	−0.109808
$773$	8.52812e14	0.111139	0.0555694	−	0.998455i	$-0.482303\pi$
$773$	8.52812e14	0.111139	0.0555694	+	0.998455i	$0.482303\pi$
$774$	−4.94220e15	−0.639506
$775$	8.48095e15	1.08965
$776$	7.05162e14	0.0899600
$777$	3.77728e16	4.78480
$778$	7.80594e15	0.981832
$779$	−1.43455e15	−0.179167
$780$	8.98401e15	1.11417
$781$	−5.39729e15	−0.664653
$782$	−9.22188e15	−1.12767
$783$	−2.54415e15	−0.308925
$784$	8.57291e14	0.103369
$785$	−7.20493e15	−0.862674
$786$	6.76877e15	0.804796
$787$	−8.69747e15	−1.02691	−0.513454	−	0.858117i	$-0.671634\pi$
$787$	−8.69747e15	−1.02691	−0.513454	+	0.858117i	$0.671634\pi$
$788$	3.60978e14	0.0423240
$789$	−3.83184e15	−0.446153
$790$	8.75864e15	1.01272
$791$	−2.35387e15	−0.270279
$792$	1.66789e16	1.90186
$793$	1.78180e15	0.201769
$794$	8.72163e15	0.980810
$795$	−3.74151e16	−4.17857
$796$	4.26243e15	0.472754
$797$	−5.21418e15	−0.574335	−0.287168	−	0.957880i	$-0.592714\pi$
$797$	−5.21418e15	−0.574335	−0.287168	+	0.957880i	$0.592714\pi$
$798$	−1.03968e16	−1.13732
$799$	−9.99774e15	−1.08616
$800$	−8.96678e15	−0.967479
$801$	−2.89214e15	−0.309913
$802$	1.19720e14	0.0127411
$803$	−2.80982e15	−0.296991
$804$	−1.23197e16	−1.29328
$805$	2.27535e16	2.37230
$806$	−4.72944e15	−0.489741
$807$	−2.24095e16	−2.30477
$808$	3.26644e15	0.333666
$809$	−6.31494e15	−0.640696	−0.320348	−	0.947300i	$-0.603800\pi$
$809$	−6.31494e15	−0.640696	−0.320348	+	0.947300i	$0.603800\pi$
$810$	7.42705e15	0.748425
$811$	1.44640e16	1.44768	0.723841	−	0.689967i	$-0.242375\pi$
$811$	1.44640e16	1.44768	0.723841	+	0.689967i	$0.242375\pi$
$812$	−1.97786e15	−0.196625
$813$	−2.36544e16	−2.33568
$814$	1.01476e16	0.995239
$815$	1.37222e16	1.33677
$816$	1.98590e15	0.192159
$817$	−3.83479e15	−0.368571
$818$	8.72882e15	0.833321
$819$	−2.44362e16	−2.31724
$820$	2.53874e15	0.239134
$821$	1.98550e16	1.85773	0.928865	−	0.370418i	$-0.120786\pi$
$821$	1.98550e16	1.85773	0.928865	+	0.370418i	$0.120786\pi$
$822$	−1.70479e16	−1.58444
$823$	1.31546e16	1.21445	0.607226	−	0.794529i	$-0.292282\pi$
$823$	1.31546e16	1.21445	0.607226	+	0.794529i	$0.292282\pi$
$824$	−2.89380e15	−0.265380
$825$	1.77599e16	1.61787
$826$	4.97787e15	0.450457
$827$	−1.81590e16	−1.63235	−0.816173	−	0.577808i	$-0.803908\pi$
$827$	−1.81590e16	−1.63235	−0.816173	+	0.577808i	$0.803908\pi$
$828$	−1.46877e16	−1.31155
$829$	4.17299e15	0.370167	0.185084	−	0.982723i	$-0.440744\pi$
$829$	4.17299e15	0.370167	0.185084	+	0.982723i	$0.440744\pi$
$830$	2.57159e15	0.226606
$831$	−2.49564e16	−2.18462
$832$	4.49690e15	0.391053
$833$	3.59045e16	3.10171
$834$	−8.62174e15	−0.739915
$835$	−2.60279e15	−0.221903
$836$	5.07428e15	0.429774
$837$	2.26350e16	1.90454
$838$	6.82827e15	0.570780
$839$	1.20517e16	1.00083	0.500413	−	0.865787i	$-0.333181\pi$
$839$	1.20517e16	1.00083	0.500413	+	0.865787i	$0.333181\pi$
$840$	4.69263e16	3.87151
$841$	4.20707e14	0.0344828
$842$	−6.82510e15	−0.555767
$843$	−2.10305e16	−1.70136
$844$	−9.59673e15	−0.771330
$845$	8.47717e15	0.676922
$846$	8.76480e15	0.695352
$847$	5.38432e14	0.0424397
$848$	1.35234e15	0.105903
$849$	3.80388e16	2.95961
$850$	−1.34237e16	−1.03769
$851$	−2.27909e16	−1.75045
$852$	9.80235e15	0.748019
$853$	−2.50990e16	−1.90299	−0.951496	−	0.307660i	$-0.900454\pi$
$853$	−2.50990e16	−1.90299	−0.951496	+	0.307660i	$0.900454\pi$
$854$	3.64913e15	0.274898
$855$	2.47737e16	1.85429
$856$	3.71056e15	0.275952
$857$	−2.13127e16	−1.57487	−0.787435	−	0.616397i	$-0.788592\pi$
$857$	−2.13127e16	−1.57487	−0.787435	+	0.616397i	$0.788592\pi$
$858$	−9.90386e15	−0.727151
$859$	1.97081e16	1.43775	0.718875	−	0.695139i	$-0.244657\pi$
$859$	1.97081e16	1.43775	0.718875	+	0.695139i	$0.244657\pi$
$860$	6.78649e15	0.491930
$861$	−1.04177e16	−0.750331
$862$	5.89608e14	0.0421962
$863$	−9.46935e14	−0.0673381	−0.0336690	−	0.999433i	$-0.510719\pi$
$863$	−9.46935e14	−0.0673381	−0.0336690	+	0.999433i	$0.510719\pi$
$864$	−2.39316e16	−1.69101
$865$	3.87773e15	0.272263
$866$	8.19364e15	0.571648
$867$	5.83301e16	4.04378
$868$	1.75968e16	1.21220
$869$	1.75414e16	1.20076
$870$	−3.91368e15	−0.266213
$871$	1.23669e16	0.835916
$872$	5.58683e15	0.375254
$873$	2.70346e15	0.180443
$874$	6.27309e15	0.416072
$875$	−1.67721e15	−0.110546
$876$	5.10309e15	0.334242
$877$	−2.98772e16	−1.94465	−0.972327	−	0.233625i	$-0.924941\pi$
$877$	−2.98772e16	−1.94465	−0.972327	+	0.233625i	$0.924941\pi$
$878$	1.62057e16	1.04821
$879$	−2.37290e16	−1.52525
$880$	−1.31634e15	−0.0840841
$881$	1.36351e16	0.865547	0.432773	−	0.901503i	$-0.357535\pi$
$881$	1.36351e16	0.865547	0.432773	+	0.901503i	$0.357535\pi$
$882$	−3.14767e16	−1.98569
$883$	−1.79474e16	−1.12517	−0.562583	−	0.826741i	$-0.690192\pi$
$883$	−1.79474e16	−1.12517	−0.562583	+	0.826741i	$0.690192\pi$
$884$	−1.35997e16	−0.847310
$885$	−1.78948e16	−1.10800
$886$	−1.58273e15	−0.0973914
$887$	1.46075e16	0.893295	0.446647	−	0.894710i	$-0.352618\pi$
$887$	1.46075e16	0.893295	0.446647	+	0.894710i	$0.352618\pi$
$888$	−4.70036e16	−2.85667
$889$	1.72967e15	0.104473
$890$	−2.18600e15	−0.131222
$891$	1.48746e16	0.887395
$892$	−1.44413e16	−0.856248
$893$	6.80086e15	0.400757
$894$	1.01630e16	0.595206
$895$	−5.55793e15	−0.323509
$896$	−1.96359e16	−1.13595
$897$	2.22436e16	1.27893
$898$	−1.40594e16	−0.803431
$899$	−3.74298e15	−0.212588
$900$	−2.13799e16	−1.20690
$901$	5.66379e16	3.17776
$902$	−2.79868e15	−0.156069
$903$	−2.78482e16	−1.54353
$904$	2.92910e15	0.161364
$905$	−2.52622e16	−1.38326
$906$	−8.57971e15	−0.466947
$907$	−2.44685e16	−1.32363	−0.661817	−	0.749665i	$-0.730214\pi$
$907$	−2.44685e16	−1.32363	−0.661817	+	0.749665i	$0.730214\pi$
$908$	5.34849e15	0.287580
$909$	1.25229e16	0.669274
$910$	−1.84699e16	−0.981153
$911$	1.31818e16	0.696025	0.348013	−	0.937490i	$-0.386857\pi$
$911$	1.31818e16	0.696025	0.348013	+	0.937490i	$0.386857\pi$
$912$	−1.35089e15	−0.0709004
$913$	5.15027e15	0.268683
$914$	1.73317e16	0.898749
$915$	−1.31181e16	−0.676170
$916$	−2.83833e15	−0.145424
$917$	2.52812e16	1.28756
$918$	−3.58267e16	−1.81373
$919$	2.13683e16	1.07531	0.537656	−	0.843164i	$-0.319310\pi$
$919$	2.13683e16	1.07531	0.537656	+	0.843164i	$0.319310\pi$
$920$	−2.83139e16	−1.41634
$921$	−4.01062e16	−1.99427
$922$	−8.72386e15	−0.431210
$923$	−9.83996e15	−0.483486
$924$	3.68493e16	1.79984
$925$	−3.31753e16	−1.61077
$926$	3.36297e15	0.162316
$927$	−1.10943e16	−0.532305
$928$	3.95740e15	0.188754
$929$	−3.55257e16	−1.68444	−0.842221	−	0.539133i	$-0.818752\pi$
$929$	−3.55257e16	−1.68444	−0.842221	+	0.539133i	$0.818752\pi$
$930$	3.48195e16	1.64122
$931$	−2.44237e16	−1.14443
$932$	2.17052e16	1.01106
$933$	−4.16012e15	−0.192644
$934$	1.37278e16	0.631963
$935$	−5.51301e16	−2.52305
$936$	3.04078e16	1.38346
$937$	−2.34019e16	−1.05848	−0.529240	−	0.848472i	$-0.677523\pi$
$937$	−2.34019e16	−1.05848	−0.529240	+	0.848472i	$0.677523\pi$
$938$	2.53276e16	1.13888
$939$	3.88279e16	1.73573
$940$	−1.20356e16	−0.534889
$941$	3.91245e16	1.72865	0.864323	−	0.502937i	$-0.167747\pi$
$941$	3.91245e16	1.72865	0.864323	+	0.502937i	$0.167747\pi$
$942$	−1.44251e16	−0.633635
$943$	6.28569e15	0.274498
$944$	6.46793e14	0.0280815
$945$	8.83965e16	3.81558
$946$	−7.48135e15	−0.321054
$947$	3.09483e15	0.132042	0.0660209	−	0.997818i	$-0.478970\pi$
$947$	3.09483e15	0.132042	0.0660209	+	0.997818i	$0.478970\pi$
$948$	−3.18581e16	−1.35137
$949$	−5.12267e15	−0.216039
$950$	9.13132e15	0.382872
$951$	6.68069e16	2.78502
$952$	−7.10356e16	−2.94424
$953$	4.66240e15	0.192132	0.0960658	−	0.995375i	$-0.469374\pi$
$953$	4.66240e15	0.192132	0.0960658	+	0.995375i	$0.469374\pi$
$954$	−4.96532e16	−2.03438
$955$	6.21926e16	2.53350
$956$	−1.13822e16	−0.461007
$957$	−7.83814e15	−0.315644
$958$	6.49234e15	0.259951
$959$	−6.36736e16	−2.53488
$960$	−3.31076e16	−1.31050
$961$	7.89243e15	0.310622
$962$	1.85003e16	0.723963
$963$	1.42256e16	0.553510
$964$	−2.17033e16	−0.839657
$965$	−6.18309e15	−0.237851
$966$	4.55551e16	1.74246
$967$	3.18671e16	1.21198	0.605992	−	0.795471i	$-0.292776\pi$
$967$	3.18671e16	1.21198	0.605992	+	0.795471i	$0.292776\pi$
$968$	−6.70012e14	−0.0253377
$969$	−5.65771e16	−2.12745
$970$	2.04339e15	0.0764023
$971$	−6.29061e14	−0.0233877	−0.0116938	−	0.999932i	$-0.503722\pi$
$971$	−6.29061e14	−0.0233877	−0.0116938	+	0.999932i	$0.503722\pi$
$972$	2.00969e15	0.0742959
$973$	−3.22020e16	−1.18376
$974$	4.83087e15	0.176584
$975$	3.23785e16	1.17688
$976$	4.74145e14	0.0171371
$977$	8.87319e15	0.318904	0.159452	−	0.987206i	$-0.449027\pi$
$977$	8.87319e15	0.318904	0.159452	+	0.987206i	$0.449027\pi$
$978$	2.74734e16	0.981857
$979$	−4.37803e15	−0.155587
$980$	4.32229e16	1.52746
$981$	2.14188e16	0.752691
$982$	2.05147e16	0.716888
$983$	−2.31368e16	−0.804004	−0.402002	−	0.915639i	$-0.631686\pi$
$983$	−2.31368e16	−0.804004	−0.402002	+	0.915639i	$0.631686\pi$
$984$	1.29635e16	0.447970
$985$	2.66782e15	0.0916764
$986$	5.92441e15	0.202452
$987$	4.93877e16	1.67832
$988$	9.25108e15	0.312629
$989$	1.68028e16	0.564678
$990$	4.83314e16	1.61523
$991$	−2.13231e16	−0.708672	−0.354336	−	0.935118i	$-0.615293\pi$
$991$	−2.13231e16	−0.708672	−0.354336	+	0.935118i	$0.615293\pi$
$992$	−3.52085e16	−1.16368
$993$	5.84413e16	1.92088
$994$	−2.01523e16	−0.658718
$995$	3.15017e16	1.02402
$996$	−9.35373e15	−0.302384
$997$	−6.18696e16	−1.98909	−0.994543	−	0.104324i	$-0.966732\pi$
$997$	−6.18696e16	−1.98909	−0.994543	+	0.104324i	$0.966732\pi$
$998$	2.40526e15	0.0769032
$999$	−8.85421e16	−2.81540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.b.1.6	✓	14
3.2	odd	2		261.12.a.e.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.b.1.6	✓	14	1.1	even	1	trivial
261.12.a.e.1.9		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-26.9644 q^{2} +724.855 q^{3} -1320.92 q^{4} -9762.32 q^{5} -19545.3 q^{6} -73001.2 q^{7} +90841.0 q^{8} +348267. q^{9} +O(q^{10})\)	\(q-26.9644 q^{2} +724.855 q^{3} -1320.92 q^{4} -9762.32 q^{5} -19545.3 q^{6} -73001.2 q^{7} +90841.0 q^{8} +348267. q^{9} +263235. q^{10} +527196. q^{11} -957474. q^{12} +961147. q^{13} +1.96844e6 q^{14} -7.07626e6 q^{15} +255766. q^{16} +1.07118e7 q^{17} -9.39083e6 q^{18} -7.28662e6 q^{19} +1.28952e7 q^{20} -5.29153e7 q^{21} -1.42156e7 q^{22} +3.19275e7 q^{23} +6.58465e7 q^{24} +4.64747e7 q^{25} -2.59168e7 q^{26} +1.24037e8 q^{27} +9.64287e7 q^{28} -2.05111e7 q^{29} +1.90807e8 q^{30} +1.82485e8 q^{31} -1.92939e8 q^{32} +3.82141e8 q^{33} -2.88838e8 q^{34} +7.12661e8 q^{35} -4.60033e8 q^{36} -7.13835e8 q^{37} +1.96480e8 q^{38} +6.96692e8 q^{39} -8.86819e8 q^{40} +1.96874e8 q^{41} +1.42683e9 q^{42} +5.26279e8 q^{43} -6.96384e8 q^{44} -3.39989e9 q^{45} -8.60906e8 q^{46} -9.33336e8 q^{47} +1.85393e8 q^{48} +3.35185e9 q^{49} -1.25316e9 q^{50} +7.76452e9 q^{51} -1.26960e9 q^{52} +5.28742e9 q^{53} -3.34459e9 q^{54} -5.14666e9 q^{55} -6.63151e9 q^{56} -5.28174e9 q^{57} +5.53072e8 q^{58} +2.52885e9 q^{59} +9.34717e9 q^{60} +1.85382e9 q^{61} -4.92061e9 q^{62} -2.54239e10 q^{63} +4.67868e9 q^{64} -9.38302e9 q^{65} -1.03042e10 q^{66} +1.28669e10 q^{67} -1.41495e10 q^{68} +2.31428e10 q^{69} -1.92165e10 q^{70} -1.02377e10 q^{71} +3.16369e10 q^{72} -5.32974e9 q^{73} +1.92482e10 q^{74} +3.36874e10 q^{75} +9.62503e9 q^{76} -3.84860e10 q^{77} -1.87859e10 q^{78} +3.32730e10 q^{79} -2.49687e9 q^{80} +2.82145e10 q^{81} -5.30860e9 q^{82} +9.76917e9 q^{83} +6.98968e10 q^{84} -1.04572e11 q^{85} -1.41908e10 q^{86} -1.48676e10 q^{87} +4.78910e10 q^{88} -8.30436e9 q^{89} +9.16762e10 q^{90} -7.01650e10 q^{91} -4.21736e10 q^{92} +1.32275e11 q^{93} +2.51669e10 q^{94} +7.11343e10 q^{95} -1.39853e11 q^{96} +7.76260e9 q^{97} -9.03809e10 q^{98} +1.83605e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more